**A tessellation is a pattern of geometric shapes that can completely cover a surface without the shapes overlapping one another or leaving any gaps.** Tessellations may also be called tilings, as the individual shapes in the pattern resemble tiles.

Regular tessellations are tessellations made up of regular polygons, or shapes whose sides and angles are all equal. A simple example of a regular tessellation is a pattern made up of squares that touch on each side, as on a checkerboard. Semi-regular, or Archimedean, tessellations are made up of two or more different kinds of regular polygons such that the pattern at each vertex where the shapes meet is the same.